메뉴 건너뛰기




Volumn 48, Issue 2, 2010, Pages 408-427

Finite element approximation of the linear stochastic wave equation with additive noise

Author keywords

A priori error estimate; Additive noise; Finite element method; Stability; Stochastic wave equation; Strong convergence; Wiener process

Indexed keywords

A PRIORI ERROR ESTIMATE; APRIORI; STOCHASTIC WAVE EQUATIONS; STRONG CONVERGENCE; WIENER PROCESS;

EID: 77954184528     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/090772241     Document Type: Article
Times cited : (83)

References (22)
  • 1
    • 34547655997 scopus 로고    scopus 로고
    • Modeling with itô stochastic differential equations
    • Springer, Dordrecht, The Netherlands
    • E. J. ALLEN, Modeling with Itô Stochastic Di.erential Equations, Math. Model. Theory Appl. 22, Springer, Dordrecht, The Netherlands, 2007.
    • (2007) Math. Model. Theory Appl. , vol.22
    • Allen, E.J.1
  • 2
    • 0037606706 scopus 로고    scopus 로고
    • Finite element and di.erence approximation of some linear stochastic partial di.erential equations
    • E. J. ALLEN, S. J. NOVOSEL, AND Z. ZHANG, Finite element and di.erence approximation of some linear stochastic partial di.erential equations, Stochastics Stochastics Rep., 64 (1998), pp. 117-142.
    • (1998) Stochastics Stochastics Rep. , vol.64 , pp. 117-142
    • Allen, E.J.1    Novosel, S.J.2    Zhang, Z.3
  • 3
    • 0016994245 scopus 로고
    • Error estimates for.nite element methods for second order hyperbolic equations
    • G. A. BAKER, Error estimates for.nite element methods for second order hyperbolic equations, SIAM J. Numer. Anal., 13 (1976), pp. 564-576.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 564-576
    • Baker, G.A.1
  • 6
    • 0038620976 scopus 로고    scopus 로고
    • Numerical approximation of some linear stochastic partial di.erential equations driven by special additive noises
    • Q. DU AND T. ZHANG, Numerical approximation of some linear stochastic partial di.erential equations driven by special additive noises, SIAM J. Numer. Anal., 40 (2002), pp. 1421-1445.
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 1421-1445
    • Du, Q.1    Zhang, T.2
  • 7
    • 0000807980 scopus 로고
    • L2-estimates for Galerkin methods for second order hyperbolic equations
    • T. DUPONT, L2-estimates for Galerkin methods for second order hyperbolic equations, SIAM J. Numer. Anal., 10 (1973), pp. 880-889.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 880-889
    • Dupont, T.1
  • 8
    • 67349263036 scopus 로고    scopus 로고
    • Rate of weak convergence of the.nite element method for the stochastic heat equation with additive noise
    • M. GEISSERT, M. KOVÁCS, AND S. LARSSON, Rate of weak convergence of the.nite element method for the stochastic heat equation with additive noise, BIT, 49 (2009), pp. 343-356.
    • (2009) BIT , vol.49 , pp. 343-356
    • Geissert, M.1    Kovács, M.2    Larsson, S.3
  • 9
    • 4544297429 scopus 로고    scopus 로고
    • Approximations of stochastic partial di.erential equations
    • in Stochastic Partial Di.erential Equations and Applications Trento, 2002, Dekker, New York
    • I. GYÖNGY, Approximations of stochastic partial di.erential equations, in Stochastic Partial Di.erential Equations and Applications (Trento, 2002), Lect. Notes Pure Appl. Math. 227, Dekker, New York, 2002, pp. 287-307.
    • (2002) Lect. Notes Pure Appl. Math. , vol.227 , pp. 287-307
    • Gyöngy, I.1
  • 11
    • 74149086958 scopus 로고    scopus 로고
    • Strong convergence of the.nite element method with truncated noise for semilinear parabolic stochastic equations with additive noise
    • M. KOVÁCS, S. LARSSON, AND F. LINDGREN, Strong convergence of the.nite element method with truncated noise for semilinear parabolic stochastic equations with additive noise, Numer. Algorithms, 53 (2010), pp. 309-320.
    • (2010) Numer. Algorithms , vol.53 , pp. 309-320
    • Kovács, M.1    Larsson, S.2    Lindgren, F.3
  • 12
    • 11144345650 scopus 로고    scopus 로고
    • Exact and fast numerical algorithms for the stochastic wave equation
    • A. MARTIN, S. M. PRIGARIN, AND G. WINKLER, Exact and fast numerical algorithms for the stochastic wave equation, Int. J. Comput. Math., 80 (2003), pp. 1535-1541.
    • (2003) Int. J. Comput. Math. , vol.80 , pp. 1535-1541
    • Martin, A.1    Prigarin, S.M.2    Winkler, G.3
  • 13
    • 34547290416 scopus 로고    scopus 로고
    • A concise course on stochastic partial differential equations
    • Springer, Berlin
    • C. PRÉVÔT AND M. RÖCKNER, A Concise Course on Stochastic Partial Di.erential Equations, Lecture Notes in Math. 1905, Springer, Berlin, 2007.
    • (2007) Lecture Notes in Math. , vol.1905
    • Prévôt, C.1    Röckner, M.2
  • 14
    • 33745094134 scopus 로고    scopus 로고
    • Space semi-discretisations for a stochastic wave equation
    • L. QUER-SARDANYONS AND M. SANZ-SOLÉ, Space semi-discretisations for a stochastic wave equation, Potential Anal., 24 (2006), pp. 303-332.
    • (2006) Potential Anal. , vol.24 , pp. 303-332
    • Quer-Sardanyons, L.1    Sanz-Solé, M.2
  • 15
    • 0022048158 scopus 로고
    • On convergence of the.nite element method for the wave equation
    • J. RAUCH, On convergence of the.nite element method for the wave equation, SIAMJ. Numer. Anal., 22 (1985), pp. 245-249.
    • (1985) SIAMJ. Numer. Anal. , vol.22 , pp. 245-249
    • Rauch, J.1
  • 16
    • 71149106146 scopus 로고    scopus 로고
    • Weak approximations of solutions of a.rst order hyperbolic stochastic partial differential equation
    • C. ROTH, Weak approximations of solutions of a.rst order hyperbolic stochastic partial differential equation, Monte Carlo Methods Appl., 13 (2007), pp. 117-133.
    • (2007) Monte Carlo Methods Appl. , vol.13 , pp. 117-133
    • Roth, C.1
  • 17
    • 33746346426 scopus 로고    scopus 로고
    • Karhunen-Loève approximation of random.elds by generalized fast multipole methods
    • C. SCHWAB AND R. A. TODOR, Karhunen-Loève approximation of random.elds by generalized fast multipole methods, J. Comput. Phys., 217 (2006), pp. 100-122.
    • (2006) J. Comput. Phys. , vol.217 , pp. 100-122
    • Schwab, C.1    Todor, R.A.2
  • 19
    • 0000659593 scopus 로고
    • An introduction to stochastic partial di.erential equations
    • in École d'été de probabilités de Saint-Flour, XIV-1984, Springer, Berlin
    • J. B. WALSH, An introduction to stochastic partial di.erential equations, in École d'été de probabilités de Saint-Flour, XIV-1984, Lecture Notes in Math. 1180, Springer, Berlin, 1986, pp. 265-439.
    • (1986) Lecture Notes in Math. , vol.1180 , pp. 265-439
    • Walsh, J.B.1
  • 20
    • 33846158441 scopus 로고    scopus 로고
    • On numerical solutions of the stochastic wave equation
    • J. B. WALSH, On numerical solutions of the stochastic wave equation, Illinois J. Math., 50 (2006), pp. 991-1018.
    • (2006) Illinois J. Math. , vol.50 , pp. 991-1018
    • Walsh, J.B.1
  • 21
    • 18244393447 scopus 로고    scopus 로고
    • Semidiscrete Galerkin approximation for a linear stochastic parabolic partial di.erential equation driven by an additive noise
    • Y. YAN, Semidiscrete Galerkin approximation for a linear stochastic parabolic partial di.erential equation driven by an additive noise, BIT, 44 (2004), pp. 829-847.
    • (2004) BIT , vol.44 , pp. 829-847
    • Yan, Y.1
  • 22
    • 33747184742 scopus 로고    scopus 로고
    • Galerkin. nite element methods for stochastic parabolic partial di.erential equations
    • Y. YAN, Galerkin. nite element methods for stochastic parabolic partial di.erential equations, SIAM J. Numer. Anal., 43 (2005), pp. 1363-1384.
    • (2005) SIAM J. Numer. Anal. , vol.43 , pp. 1363-1384
    • Yan, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.